Effects of density and size on terminal velocity of a vertically falling spherical particles in Newtonian fluid by diagonal Pade’ approximant

Abstract

In this paper, the effects of physical parameters on terminal velocity of vertically falling spherical particles made of Glass, Iron, Copper and Silver with different diameters (D=0.1mm, 0.2mm, 0.5mm &1mm) in Newtonian fluid is discussed using Diagonal Pade’ [2/2] approximant and Collocation Method (CM) and compare the results with Runge-Kutta 4th order method to verify the accuracy. It observed that the Diagonal Pade’ approximant which was used to solve nonlinear differential equations is more accurate and simpler as compared to Collocation Method (CM), Homotopy Perturbation Method (HPM), Akbari-Ganji’s Method (AGM), and Varinational Iteration Method (VIM) etc. The Outcomes clearly demonstrate that the time of reaching the particles at terminal velocity in a vertically falling procedure is significantly increased with growing the size and density of a particle and the acceleration period for smaller and lighter particles is shorter. Further from these four particles, the glass’s particles have low velocity and reaches early at terminal velocity due to its lowest density as compared to other. To obtain the results for all different methods, the symbolic calculus software MATLAB was used.